UTI analysis
April 24, 2025
Static analysis
- Dataset contains many tongue contours like this
- e.g. all contours at gesture mid-time
- One “data point” is a whole contour
- knots (1-11) are provided by UTI post-processing software
- Static analysis = no time involved
- GOAL: statistical analysis
- e.g. how contour shape varies with respect to conditions A and B
Dynamic analysis
- Dataset contains many sequences of tongue contours like this
- e.g. contour sequences represent gestures form onset to offset
- One “data point” is a sequence of contours, or a clip
- Dynamic analysis = time axis should be included in the model
- GOAL: statistical analysis
- e.g. how dynamic gesture varies with respect to conditions A and B
Roadmap
- Static or dynamic?
- i.e. do we need the time axis?
- Choose geometrical parametrisation of contours
- radial coordinates
- 2-dim. trajectory
- Choose statistical modelling framework
Parametrization
- static case
y ~ x: a bad idea
- Non-unicity of y values at a given x!
radius ~ angle: PROS
- Simplest geometry
- one indep. variable: angle
- one dep. variable: radius
- Plugs in to simplest model
- Solves most of the non-unicity issues
radius ~ angle: CONS
- Non-unicity at curled tongue tip
- Requires choosing origin
- Does not use knots properly
Linear angle normalization
Procrustean angle interpolation
(x, y) ~ knot: PROS
- Solves all non-unicity problems
- Proper use of knots
(x, y) ~ knot: CONS
- Complex model:
- Two equations, one for x, one for y
- Requires multivariate models
Parametrization
- dynamic case
radius ~ angle * time
- Simplest geometry
- Yet requires a 2D support
- Same pros & cons as static counterpart
(x, y) ~ knot * time
- The most complex geometry
- 2D support (knot, time)
- 2 response variables (x, y)
- Requires most complex models
- All pros and cons of static counterpart